Question: Solve for $x$ and $y$ using elimination. ${x+6y = 25}$ ${x+5y = 21}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-x-6y = -25}$ $x+5y = 21$ Add the top and bottom equations together. $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {x+6y = 25}\thinspace$ to find $x$ ${x + 6}{(4)}{= 25}$ $x+24 = 25$ $x+24{-24} = 25{-24}$ ${x = 1}$ You can also plug ${y = 4}$ into $\thinspace {x+5y = 21}\thinspace$ and get the same answer for $x$ : ${x + 5}{(4)}{= 21}$ ${x = 1}$